Anders, are you still seeing this issue with currently-supported versions of Ubuntu? I have argued elsewhere that the correct thing to do for 18.04 is to forcibly remove resolvconf on upgrades, switching /etc/resolv.conf to exclusively point to /run/systemd/resolve/stub-resolv.conf. In the common case, however, this should not make a difference. What other sources of DNS settings do you have that are feeding directly to resolvconf instead of resolved in 16.10 and later?
Anders, are you still seeing this issue with currently-supported versions of Ubuntu? I have argued elsewhere that the correct thing to do for 18.04 is to forcibly remove resolvconf on upgrades, switching /etc/resolv.conf to exclusively point to /run/systemd/ resolve/ stub-resolv. conf. In the common case, however, this should not make a difference. What other sources of DNS settings do you have that are feeding directly to resolvconf instead of resolved in 16.10 and later?